I have no idea what the part is but I am thinking it just maybe called the unsingle barrel hanger. Anyway... its the part the connects the end of the barrel to the unsingle rib.

I have the older version (its ribbed not the smooth solid one).

Should there be any play between the hanger and the barrel?

I have had the gun about a year as I bought it used form Chris Maest and have never noticed it before, but there is definitely some play. If I attempt to pull the rib up (away from the barrel) I can feel a little play between them.

I don't remember any play. I remember the connection to be tight as a drum but then again I may have never noticed. I can't believe there should be any play between the rib and barrel so i am kind of concerned.

Any answers? Just call Chris and have him handle it or is this something I can correct by tightening it up somehow.

There should be no play. I have the same barrel and its as solid as a rock. Your lucky you bought it from one of the very best dealers of Krieghoff's. I would email him or give him a call. I am not sure how you fix it but he sure will.